4,332 research outputs found
Reply to "Comment on 'Entropy, energy, and proximity to criticality in global earthquake populations"' by Chien-Chih Chen and Chun-Ling Chang
Uniform semiclassical approximations on a topologically non-trivial configuration space: The hydrogen atom in an electric field
Semiclassical periodic-orbit theory and closed-orbit theory represent a
quantum spectrum as a superposition of contributions from individual classical
orbits. Close to a bifurcation, these contributions diverge and have to be
replaced with a uniform approximation. Its construction requires a normal form
that provides a local description of the bifurcation scenario. Usually, the
normal form is constructed in flat space. We present an example taken from the
hydrogen atom in an electric field where the normal form must be chosen to be
defined on a sphere instead of a Euclidean plane. In the example, the necessity
to base the normal form on a topologically non-trivial configuration space
reveals a subtle interplay between local and global aspects of the phase space
structure. We show that a uniform approximation for a bifurcation scenario with
non-trivial topology can be constructed using the established uniformization
techniques. Semiclassical photo-absorption spectra of the hydrogen atom in an
electric field are significantly improved when based on the extended uniform
approximations
Criteria for beach nourishment: biological guidelines for sabellariid worm reef
It has been the purpose of this project to provide the basic biological and geological data together with summary guidelines which will allow the Florida Dept. of Environmental Regulation and project engineers to make the necessary permitting and design decisions for beach nourishment project in worm reef areas. The present work
seeks to determine the tolerance of P. lapidosa to
sediment burial, the tolerance of these organisms to exposure to hydrogen sulfide, the tolerances of these organisms to heavy silt loads in the water, etc. (37pp.
Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems
Harmonic inversion has already been proven to be a powerful tool for the
analysis of quantum spectra and the periodic orbit orbit quantization of
chaotic systems. The harmonic inversion technique circumvents the convergence
problems of the periodic orbit sum and the uncertainty principle of the usual
Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular
and chaotic systems the technique is generalized in this paper for the
semiclassical quantization of integrable systems. Thus, harmonic inversion is
shown to be a universal tool which can be applied to a wide range of physical
systems. The method is further generalized in two directions: Firstly, the
periodic orbit quantization will be extended to include higher order hbar
corrections to the periodic orbit sum. Secondly, the use of cross-correlated
periodic orbit sums allows us to significantly reduce the required number of
orbits for semiclassical quantization, i.e., to improve the efficiency of the
semiclassical method. As a representative of regular systems, we choose the
circle billiard, whose periodic orbits and quantum eigenvalues can easily be
obtained.Comment: 21 pages, 9 figures, submitted to Eur. Phys. J.
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